A group of adults and kids went to see a movie. Tickets cost $$5.50$ each for adults and $$4.50$ each for kids, and the group paid $$48.00$ in total. There were $4$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5.5x+4.5y = 48}$ ${x = y-4}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-4}$ for $x$ in the first equation. ${5.5}{(y-4)}{+ 4.5y = 48}$ Simplify and solve for $y$ $ 5.5y-22 + 4.5y = 48 $ $ 10y-22 = 48 $ $ 10y = 70 $ $ y = \dfrac{70}{10} $ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into ${x = y-4}$ to find $x$ ${x = }{(7)}{ - 4}$ ${x = 3}$ You can also plug ${y = 7}$ into ${5.5x+4.5y = 48}$ and get the same answer for $x$ ${5.5x + 4.5}{(7)}{= 48}$ ${x = 3}$ There were $3$ adults and $7$ kids.